Get a cleaner and higher version of the file. This one is very low resolution and has a lot of noise. That is why you’re seeing some parts of the “white” show up in the engraving. If the white was a true white this wouldn’t occur.
Get a version of the file with a transparent background in PNG format.
As @killrob has mentioned, you could attempt to trace the image but I think you’ll have subpar results without a lot of hand-editing due to the low quality of the starting image.
Because the logo is a circle you could easily create a circle in LIghtBurn and then apply an image mask to eliminate the noisy background.
Depending on the look you are going for you could potentially use a different image mode and adjust the image enough to get an acceptable result. Again, not ideal.
If you can get a vector version of the logo (SVG, AI, etc.) that would probably be ideal and give you the most flexibility. The logo almost certainly originated in a vector format.